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JEE Main 2019 (10 Jan, Shift 1) · Escape Velocity

Escape Velocity question from JEE Main 2019 (10 Jan, Shift 1)

Q65JEE Main 2019 · 10 JAN · SHIFT 1Medium

Escape Velocity

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

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Answer: (a)

In orbit of radius $r$ : $v^2 = \dfrac{GM}{r}$ .
To just escape, KE must cancel the PE: $K = \dfrac{GMm}{r}$ .
$K = m\cdot\dfrac{GM}{r} = mv^2$ .
So the answer is (a) $mv^2$ .

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